Electromagnetic waves radiating away from a transmitting tower

[DottZakapa]

Homework Statement

A radio station on the surface of the earth radiates a sinusoidal wave with an average total power of 50 kw. Assuming that the transmitter radiates equally in all the directions above the ground, at a distance of 100 km from the antenna (ε0 = 8.85 10-12 C2N-1m-2)

Relevant Equations

electromagnetic waves

Homework Statement: A radio station on the surface of the Earth radiates a sinusoidal wave with an average total power of 50 kw. Assuming that the transmitter radiates equally in all the directions above the ground, at a distance of 100 km from the antenna (ε0 = 8.85 10-12 C2N-1m-2)
Homework Equations: electromagnetic waves

I divide the power by the half sphere
50000/(4πr2/2)
In such way i get the intensity per surface unity right?
which is also equal to
I=cε₀E²
Now, from this equation i solve for E if i want to get Emax right ?
In case i need Bmax i divide Emax by c
Is there any error ? because can't get the right result

 

[Doc Al]

I divide the power by the half sphere
50000m/((4πr2)/2)
In such way i get the intensity per surface unity right?

That's the right approach (but I don't know what the "m" is for in your expression).

which is also equal to
I=cε0E2

Where did you get that equation?

 

[DottZakapa]

That's the right approach (but I don't know what the "m" is for in your expression).

Where did you get that equation?

that equation comes from:

total energy density

relation between E and B

energy flow per unit area per unit time

But i realized that this leads to instantaneous intensity, in order to get the average intensity , S must be divided by 2.
Doing so you get the average intensity,

which leads to the correct result.
Thanks very kind.

 

[Doc Al]

But i realized that this leads to instantaneous intensity, in order to get the average intensity , S must be divided by 2.

Exactly. Good work!